LMFDB - Embedded newform 216.5.p.b.19.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,5,Mod(19,216)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	216.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$22.3279120261$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.35
Character	$\chi$	$=$	216.19
Dual form			216.5.p.b.91.35

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.30101 + 2.25906i) q^{2} +(5.79331 + 14.9143i) q^{4} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-14.5686 + 62.3198i) q^{8} +O(q^{10})$	\(q+(3.30101 + 2.25906i) q^{2} +(5.79331 + 14.9143i) q^{4} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-14.5686 + 62.3198i) q^{8} +(11.6869 + 0.896378i) q^{10} +(-27.1224 + 46.9774i) q^{11} +(-174.611 + 100.811i) q^{13} +(-79.5554 - 165.940i) q^{14} +(-188.875 + 172.807i) q^{16} +88.7146 q^{17} -357.083 q^{19} +(36.5537 + 29.3604i) q^{20} +(-195.656 + 93.8016i) q^{22} +(-214.383 + 123.774i) q^{23} +(-308.207 + 533.830i) q^{25} +(-804.130 - 61.6760i) q^{26} +(112.256 - 727.491i) q^{28} +(-18.7746 - 10.8395i) q^{29} +(349.016 - 201.504i) q^{31} +(-1013.86 + 143.757i) q^{32} +(292.848 + 200.411i) q^{34} -134.813 q^{35} -1263.37i q^{37} +(-1178.73 - 806.671i) q^{38} +(54.3372 + 179.496i) q^{40} +(1106.42 + 1916.37i) q^{41} +(678.384 - 1175.00i) q^{43} +(-857.765 - 132.358i) q^{44} +(-987.293 - 75.7244i) q^{46} +(-3120.48 - 1801.61i) q^{47} +(-142.209 - 246.314i) q^{49} +(-2223.34 + 1065.92i) q^{50} +(-2515.11 - 2020.17i) q^{52} +4122.82i q^{53} +158.955i q^{55} +(2014.00 - 2147.86i) q^{56} +(-37.4881 - 78.1944i) q^{58} +(2643.76 + 4579.12i) q^{59} +(-4778.25 - 2758.72i) q^{61} +(1607.31 + 123.280i) q^{62} +(-3671.51 - 1815.82i) q^{64} +(-295.410 + 511.664i) q^{65} +(3090.68 + 5353.21i) q^{67} +(513.951 + 1323.12i) q^{68} +(-445.019 - 304.551i) q^{70} -4832.30i q^{71} +9435.38 q^{73} +(2854.02 - 4170.38i) q^{74} +(-2068.69 - 5325.66i) q^{76} +(2161.26 - 1247.80i) q^{77} +(-1099.86 - 635.004i) q^{79} +(-226.125 + 715.269i) q^{80} +(-676.901 + 8825.41i) q^{82} +(-1266.75 + 2194.08i) q^{83} +(225.134 - 129.981i) q^{85} +(4893.74 - 2346.16i) q^{86} +(-2532.48 - 2374.66i) q^{88} -5907.27 q^{89} +9275.93 q^{91} +(-3087.99 - 2480.32i) q^{92} +(-6230.78 - 12996.5i) q^{94} +(-906.180 + 523.183i) q^{95} +(-928.999 + 1609.07i) q^{97} +(87.0031 - 1134.34i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 7 q^{2} + 31 q^{4} + 386 q^{8}+O(q^{10}) $ 88 * q - 7 * q^2 + 31 * q^4 + 386 * q^8	$ 88 q - 7 q^{2} + 31 q^{4} + 386 q^{8} - 36 q^{10} - 44 q^{11} + 318 q^{14} + 511 q^{16} + 1156 q^{17} + 860 q^{19} + 1164 q^{20} + 215 q^{22} + 5998 q^{25} + 5232 q^{26} - 516 q^{28} - 5227 q^{32} + 1877 q^{34} + 2508 q^{35} + 4393 q^{38} + 2274 q^{40} - 2348 q^{41} + 3500 q^{43} - 2234 q^{44} + 3576 q^{46} + 16462 q^{49} - 5785 q^{50} - 1440 q^{52} - 1146 q^{56} - 4128 q^{58} + 3508 q^{59} - 2376 q^{62} - 5510 q^{64} + 2502 q^{65} + 5132 q^{67} - 10169 q^{68} + 1134 q^{70} + 19004 q^{73} + 2946 q^{74} - 5875 q^{76} - 8592 q^{80} - 18454 q^{82} - 17090 q^{83} - 18581 q^{86} - 3253 q^{88} + 8272 q^{89} - 9612 q^{91} - 9318 q^{92} - 7590 q^{94} + 9980 q^{97} - 6826 q^{98}+O(q^{100}) $ 88 * q - 7 * q^2 + 31 * q^4 + 386 * q^8 - 36 * q^10 - 44 * q^11 + 318 * q^14 + 511 * q^16 + 1156 * q^17 + 860 * q^19 + 1164 * q^20 + 215 * q^22 + 5998 * q^25 + 5232 * q^26 - 516 * q^28 - 5227 * q^32 + 1877 * q^34 + 2508 * q^35 + 4393 * q^38 + 2274 * q^40 - 2348 * q^41 + 3500 * q^43 - 2234 * q^44 + 3576 * q^46 + 16462 * q^49 - 5785 * q^50 - 1440 * q^52 - 1146 * q^56 - 4128 * q^58 + 3508 * q^59 - 2376 * q^62 - 5510 * q^64 + 2502 * q^65 + 5132 * q^67 - 10169 * q^68 + 1134 * q^70 + 19004 * q^73 + 2946 * q^74 - 5875 * q^76 - 8592 * q^80 - 18454 * q^82 - 17090 * q^83 - 18581 * q^86 - 3253 * q^88 + 8272 * q^89 - 9612 * q^91 - 9318 * q^92 - 7590 * q^94 + 9980 * q^97 - 6826 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.30101	+	2.25906i	0.825252	+	0.564765i
$2$	3.30101	+	2.25906i	0.825252	+	0.564765i
$3$		0			0
$3$		0			0
$4$	5.79331	+	14.9143i	0.362082	+	0.932146i
$5$	2.53773	−	1.46516i	0.101509	−	0.0586064i	−0.448386	−	0.893840i	$-0.648001\pi$
$5$	2.53773	−	1.46516i	0.101509	−	0.0586064i	0.549895	+	0.835234i	$0.314668\pi$
$6$		0			0
$7$	−39.8426	−	23.0032i	−0.813115	−	0.469452i	0.0349214	−	0.999390i	$-0.488882\pi$
$7$	−39.8426	−	23.0032i	−0.813115	−	0.469452i	−0.848036	+	0.529938i	$0.822215\pi$
$8$	−14.5686	+	62.3198i	−0.227634	+	0.973747i
$9$		0			0
$10$	11.6869	+	0.896378i	0.116869	+	0.00896378i
$11$	−27.1224	+	46.9774i	−0.224152	+	0.388243i	−0.956065	−	0.293156i	$-0.905295\pi$
$11$	−27.1224	+	46.9774i	−0.224152	+	0.388243i	0.731913	+	0.681398i	$0.238628\pi$
$12$		0			0
$13$	−174.611	+	100.811i	−1.03320	+	0.596517i	−0.917899	−	0.396813i	$-0.870116\pi$
$13$	−174.611	+	100.811i	−1.03320	+	0.596517i	−0.115299	+	0.993331i	$0.536783\pi$
$14$	−79.5554	−	165.940i	−0.405895	−	0.846635i
$15$		0			0
$16$	−188.875	+	172.807i	−0.737793	+	0.675027i
$17$	88.7146			0.306971			0.153485	−	0.988151i	$-0.450950\pi$
$17$	88.7146			0.306971			0.153485	+	0.988151i	$0.450950\pi$
$18$		0			0
$19$	−357.083			−0.989149			−0.494575	−	0.869135i	$-0.664676\pi$
$19$	−357.083			−0.989149			−0.494575	+	0.869135i	$0.664676\pi$
$20$	36.5537	+	29.3604i	0.0913843	+	0.0734011i
$21$		0			0
$22$	−195.656	+	93.8016i	−0.404248	+	0.193805i
$23$	−214.383	+	123.774i	−0.405261	+	0.233977i	−0.688751	−	0.724998i	$-0.741841\pi$
$23$	−214.383	+	123.774i	−0.405261	+	0.233977i	0.283491	+	0.958975i	$0.408508\pi$
$24$		0			0
$25$	−308.207	+	533.830i	−0.493131	+	0.854127i
$26$	−804.130	−	61.6760i	−1.18954	−	0.0912367i
$27$		0			0
$28$	112.256	−	727.491i	0.143184	−	0.927922i
$29$	−18.7746	−	10.8395i	−0.0223242	−	0.0128889i	0.488796	−	0.872398i	$-0.337436\pi$
$29$	−18.7746	−	10.8395i	−0.0223242	−	0.0128889i	−0.511121	+	0.859509i	$0.670769\pi$
$30$		0			0
$31$	349.016	−	201.504i	0.363180	−	0.209682i	−0.307295	−	0.951614i	$-0.599424\pi$
$31$	349.016	−	201.504i	0.363180	−	0.209682i	0.670475	+	0.741932i	$0.266090\pi$
$32$	−1013.86	+	143.757i	−0.990097	+	0.140387i
$33$		0			0
$34$	292.848	+	200.411i	0.253328	+	0.173366i
$35$	−134.813			−0.110052
$36$		0			0
$37$		−	1263.37i		−	0.922839i	−0.887182	−	0.461419i	$-0.847340\pi$
$37$		−	1263.37i		−	0.922839i	0.887182	−	0.461419i	$-0.152660\pi$
$38$	−1178.73	−	806.671i	−0.816297	−	0.558636i
$39$		0			0
$40$	54.3372	+	179.496i	0.0339608	+	0.112185i
$41$	1106.42	+	1916.37i	0.658189	+	1.14002i	0.981084	+	0.193582i	$0.0620106\pi$
$41$	1106.42	+	1916.37i	0.658189	+	1.14002i	−0.322895	+	0.946435i	$0.604656\pi$
$42$		0			0
$43$	678.384	−	1175.00i	0.366892	−	0.635476i	−0.622185	−	0.782870i	$-0.713755\pi$
$43$	678.384	−	1175.00i	0.366892	−	0.635476i	0.989078	+	0.147393i	$0.0470884\pi$
$44$	−857.765	−	132.358i	−0.443060	−	0.0683668i
$45$		0			0
$46$	−987.293	−	75.7244i	−0.466584	−	0.0357866i
$47$	−3120.48	−	1801.61i	−1.41262	−	0.815577i	−0.416985	−	0.908913i	$-0.636913\pi$
$47$	−3120.48	−	1801.61i	−1.41262	−	0.815577i	−0.995635	+	0.0933366i	$0.970247\pi$
$48$		0			0
$49$	−142.209	−	246.314i	−0.0592292	−	0.102588i
$50$	−2223.34	+	1065.92i	−0.889338	+	0.426368i
$51$		0			0
$52$	−2515.11	−	2020.17i	−0.930144	−	0.747104i
$53$			4122.82i			1.46772i	0.679303	+	0.733858i	$0.262282\pi$
$53$			4122.82i			1.46772i	−0.679303	+	0.733858i	$0.737718\pi$
$54$		0			0
$55$			158.955i			0.0525469i
$56$	2014.00	−	2147.86i	0.642221	−	0.684905i
$57$		0			0
$58$	−37.4881	−	78.1944i	−0.0111439	−	0.0232445i
$59$	2643.76	+	4579.12i	0.759482	+	1.31546i	0.943115	+	0.332466i	$0.107881\pi$
$59$	2643.76	+	4579.12i	0.759482	+	1.31546i	−0.183634	+	0.982995i	$0.558786\pi$
$60$		0			0
$61$	−4778.25	−	2758.72i	−1.28413	−	0.741393i	−0.306530	−	0.951861i	$-0.599168\pi$
$61$	−4778.25	−	2758.72i	−1.28413	−	0.741393i	−0.977601	+	0.210468i	$0.932501\pi$
$62$	1607.31	+	123.280i	0.418136	+	0.0320706i
$63$		0			0
$64$	−3671.51	−	1815.82i	−0.896365	−	0.443317i
$65$	−295.410	+	511.664i	−0.0699194	+	0.121104i
$66$		0			0
$67$	3090.68	+	5353.21i	0.688500	+	1.19252i	0.972323	+	0.233641i	$0.0750640\pi$
$67$	3090.68	+	5353.21i	0.688500	+	1.19252i	−0.283822	+	0.958877i	$0.591603\pi$
$68$	513.951	+	1323.12i	0.111149	+	0.286142i
$69$		0			0
$70$	−445.019	−	304.551i	−0.0908203	−	0.0621532i
$71$		−	4832.30i		−	0.958600i	−0.877651	−	0.479300i	$-0.840891\pi$
$71$		−	4832.30i		−	0.958600i	0.877651	−	0.479300i	$-0.159109\pi$
$72$		0			0
$73$	9435.38			1.77057			0.885286	−	0.465047i	$-0.153963\pi$
$73$	9435.38			1.77057			0.885286	+	0.465047i	$0.153963\pi$
$74$	2854.02	−	4170.38i	0.521187	−	0.761574i
$75$		0			0
$76$	−2068.69	−	5325.66i	−0.358153	−	0.922032i
$77$	2161.26	−	1247.80i	0.364523	−	0.210457i
$78$		0			0
$79$	−1099.86	−	635.004i	−0.176231	−	0.101747i	0.409290	−	0.912405i	$-0.365777\pi$
$79$	−1099.86	−	635.004i	−0.176231	−	0.101747i	−0.585521	+	0.810657i	$0.699110\pi$
$80$	−226.125	+	715.269i	−0.0353320	+	0.111761i
$81$		0			0
$82$	−676.901	+	8825.41i	−0.100669	+	1.31252i
$83$	−1266.75	+	2194.08i	−0.183881	+	0.318490i	−0.943199	−	0.332229i	$-0.892199\pi$
$83$	−1266.75	+	2194.08i	−0.183881	+	0.318490i	0.759318	+	0.650720i	$0.225533\pi$
$84$		0			0
$85$	225.134	−	129.981i	0.0311604	−	0.0179904i
$86$	4893.74	−	2346.16i	0.661673	−	0.317220i
$87$		0			0
$88$	−2532.48	−	2374.66i	−0.327025	−	0.306645i
$89$	−5907.27			−0.745773			−0.372887	−	0.927877i	$-0.621632\pi$
$89$	−5907.27			−0.745773			−0.372887	+	0.927877i	$0.621632\pi$
$90$		0			0
$91$	9275.93			1.12015
$92$	−3087.99	−	2480.32i	−0.364839	−	0.293043i
$93$		0			0
$94$	−6230.78	−	12996.5i	−0.705159	−	1.47085i
$95$	−906.180	+	523.183i	−0.100408	+	0.0579704i
$96$		0			0
$97$	−928.999	+	1609.07i	−0.0987351	+	0.171014i	−0.911161	−	0.412050i	$-0.864813\pi$
$97$	−928.999	+	1609.07i	−0.0987351	+	0.171014i	0.812426	+	0.583064i	$0.198146\pi$
$98$	87.0031	−	1134.34i	0.00905905	−	0.118112i
$99$		0			0
$100$	−9747.25	−	1504.06i	−0.974725	−	0.150406i
$101$	13841.8	+	7991.56i	1.35690	+	0.783409i	0.989205	−	0.146536i	$-0.0468123\pi$
$101$	13841.8	+	7991.56i	1.35690	+	0.783409i	0.367699	+	0.929945i	$0.380146\pi$
$102$		0			0
$103$	17094.2	−	9869.37i	1.61130	−	0.930283i	0.622227	−	0.782837i	$-0.286228\pi$
$103$	17094.2	−	9869.37i	1.61130	−	0.930283i	0.989070	−	0.147445i	$-0.0471051\pi$
$104$	−3738.72	−	12350.4i	−0.345665	−	1.14186i
$105$		0			0
$106$	−9313.68	+	13609.4i	−0.828914	+	1.21124i
$107$	−8611.81			−0.752189			−0.376095	−	0.926581i	$-0.622733\pi$
$107$	−8611.81			−0.752189			−0.376095	+	0.926581i	$0.622733\pi$
$108$		0			0
$109$			19759.0i			1.66307i	0.555470	+	0.831537i	$0.312539\pi$
$109$			19759.0i			1.66307i	−0.555470	+	0.831537i	$0.687461\pi$
$110$	−359.088	+	524.710i	−0.0296767	+	0.0433645i
$111$		0			0
$112$	11500.4	−	2540.35i	0.916804	−	0.202516i
$113$	8203.89	+	14209.6i	0.642485	+	1.11282i	0.984876	+	0.173259i	$0.0554297\pi$
$113$	8203.89	+	14209.6i	0.642485	+	1.11282i	−0.342392	+	0.939557i	$0.611237\pi$
$114$		0			0
$115$	−362.697	+	628.210i	−0.0274251	+	0.0475017i
$116$	52.8973	−	342.808i	0.00393113	−	0.0254762i
$117$		0			0
$118$	−1617.44	+	21088.1i	−0.116162	+	1.51451i
$119$	−3534.62	−	2040.72i	−0.249603	−	0.144108i
$120$		0			0
$121$	5849.25	+	10131.2i	0.399512	+	0.691975i
$122$	−9540.93	−	19900.9i	−0.641019	−	1.33707i
$123$		0			0
$124$	5027.26	+	4037.96i	0.326955	+	0.262615i
$125$			3637.74i			0.232815i
$126$		0			0
$127$			190.402i			0.0118049i	0.999983	+	0.00590247i	$0.00187883\pi$
$127$			190.402i			0.0118049i	−0.999983	+	0.00590247i	$0.998121\pi$
$128$	−8017.64	−	14288.2i	−0.489358	−	0.872083i
$129$		0			0
$130$	−2131.03	+	1021.66i	−0.126096	+	0.0604533i
$131$	5339.62	+	9248.49i	0.311148	+	0.538925i	0.978611	−	0.205718i	$-0.0659530\pi$
$131$	5339.62	+	9248.49i	0.311148	+	0.538925i	−0.667463	+	0.744643i	$0.732620\pi$
$132$		0			0
$133$	14227.1	+	8214.03i	0.804292	+	0.464358i
$134$	−1890.86	+	24653.0i	−0.105305	+	1.37297i
$135$		0			0
$136$	−1292.45	+	5528.67i	−0.0698771	+	0.298912i
$137$	2673.96	−	4631.43i	0.142467	−	0.246759i	−0.785958	−	0.618280i	$-0.787830\pi$
$137$	2673.96	−	4631.43i	0.142467	−	0.246759i	0.928425	+	0.371520i	$0.121163\pi$
$138$		0			0
$139$	−4160.16	−	7205.61i	−0.215318	−	0.372942i	0.738053	−	0.674743i	$-0.235746\pi$
$139$	−4160.16	−	7205.61i	−0.215318	−	0.372942i	−0.953371	+	0.301801i	$0.902412\pi$
$140$	−781.014	−	2010.65i	−0.0398477	−	0.102584i
$141$		0			0
$142$	10916.5	−	15951.5i	0.541383	−	0.791086i
$143$		−	10937.0i		−	0.534842i
$144$		0			0
$145$	−63.5266			−0.00302148
$146$	31146.3	+	21315.1i	1.46117	+	0.999956i
$147$		0			0
$148$	18842.3	−	7319.07i	0.860220	−	0.334143i
$149$	8232.13	−	4752.82i	0.370800	−	0.214082i	−0.303008	−	0.952988i	$-0.597991\pi$
$149$	8232.13	−	4752.82i	0.370800	−	0.214082i	0.673808	+	0.738907i	$0.264658\pi$
$150$		0			0
$151$	−23033.8	−	13298.5i	−1.01021	−	0.583244i	−0.0989556	−	0.995092i	$-0.531550\pi$
$151$	−23033.8	−	13298.5i	−1.01021	−	0.583244i	−0.911253	+	0.411848i	$0.864884\pi$
$152$	5202.20	−	22253.3i	0.225164	−	0.963181i
$153$		0			0
$154$	9953.18	+	763.400i	0.419682	+	0.0321892i
$155$	590.472	−	1022.73i	0.0245774	−	0.0425693i
$156$		0			0
$157$	−14257.2	+	8231.41i	−0.578410	+	0.333945i	−0.760501	−	0.649336i	$-0.775047\pi$
$157$	−14257.2	+	8231.41i	−0.578410	+	0.333945i	0.182091	+	0.983282i	$0.441713\pi$
$158$	−2196.13	−	4580.80i	−0.0879720	−	0.183496i
$159$		0			0
$160$	−2362.27	+	1850.28i	−0.0922763	+	0.0722766i
$161$	11388.8			0.439365
$162$		0			0
$163$	−6664.66			−0.250843			−0.125422	−	0.992104i	$-0.540028\pi$
$163$	−6664.66			−0.250843			−0.125422	+	0.992104i	$0.540028\pi$
$164$	−22171.6	+	27603.6i	−0.824344	+	1.02631i
$165$		0			0
$166$	−9138.12	+	4381.01i	−0.331620	+	0.158986i
$167$	19196.1	−	11082.8i	0.688302	−	0.397391i	−0.114674	−	0.993403i	$-0.536582\pi$
$167$	19196.1	−	11082.8i	0.688302	−	0.397391i	0.802976	+	0.596012i	$0.203249\pi$
$168$		0			0
$169$	6045.39	−	10470.9i	0.211666	−	0.366616i
$170$	1036.80	+	79.5218i	0.0358755	+	0.00275162i
$171$		0			0
$172$	21454.4	+	3310.54i	0.725202	+	0.111903i
$173$	9709.71	+	5605.90i	0.324425	+	0.187307i	0.653363	−	0.757045i	$-0.273357\pi$
$173$	9709.71	+	5605.90i	0.324425	+	0.187307i	−0.328938	+	0.944351i	$0.606691\pi$
$174$		0			0
$175$	24559.5	−	14179.5i	0.801944	−	0.463002i
$176$	−2995.26	−	13559.8i	−0.0966963	−	0.437752i
$177$		0			0
$178$	−19499.9	−	13344.9i	−0.615451	−	0.421186i
$179$	16987.5			0.530179			0.265090	−	0.964224i	$-0.414598\pi$
$179$	16987.5			0.530179			0.265090	+	0.964224i	$0.414598\pi$
$180$		0			0
$181$			48494.7i			1.48026i	0.672465	+	0.740129i	$0.265236\pi$
$181$			48494.7i			1.48026i	−0.672465	+	0.740129i	$0.734764\pi$
$182$	30619.9	+	20954.9i	0.924402	+	0.632619i
$183$		0			0
$184$	−4590.31	−	15163.5i	−0.135583	−	0.447883i
$185$	−1851.03	−	3206.08i	−0.0540842	−	0.0936766i
$186$		0			0
$187$	−2406.15	+	4167.58i	−0.0688082	+	0.119179i
$188$	8791.91	−	56977.1i	0.248753	−	1.61207i
$189$		0			0
$190$	−4173.21	−	320.081i	−0.115601	−	0.00886652i
$191$	−31625.9	−	18259.2i	−0.866915	−	0.500514i	−0.000593302	−	1.00000i	$-0.500189\pi$
$191$	−31625.9	−	18259.2i	−0.866915	−	0.500514i	−0.866322	+	0.499486i	$0.833522\pi$
$192$		0			0
$193$	−12557.9	−	21750.9i	−0.337133	−	0.583932i	0.646759	−	0.762694i	$-0.276124\pi$
$193$	−12557.9	−	21750.9i	−0.337133	−	0.583932i	−0.983892	+	0.178762i	$0.942791\pi$
$194$	−6701.62	+	3212.90i	−0.178064	+	0.0853677i
$195$		0			0
$196$	2849.75	−	3547.93i	0.0741812	−	0.0923556i
$197$			28539.7i			0.735388i	0.929947	+	0.367694i	$0.119853\pi$
$197$			28539.7i			0.735388i	−0.929947	+	0.367694i	$0.880147\pi$
$198$		0			0
$199$		−	63914.2i		−	1.61395i	−0.590583	−	0.806977i	$-0.701102\pi$
$199$		−	63914.2i		−	1.61395i	0.590583	−	0.806977i	$-0.298898\pi$
$200$	−28778.0	−	26984.5i	−0.719450	−	0.674613i
$201$		0			0
$202$	27638.4	+	57649.6i	0.677346	+	1.41284i
$203$	498.687	+	863.752i	0.0121014	+	0.0209603i
$204$		0			0
$205$	5615.57	+	3242.15i	0.133624	+	0.0771481i
$206$	78723.7	+	6038.04i	1.85512	+	0.142286i
$207$		0			0
$208$	15558.7	−	49214.7i	0.359622	−	1.13754i
$209$	9684.94	−	16774.8i	0.221720	−	0.384030i
$210$		0			0
$211$	−7822.71	−	13549.3i	−0.175708	−	0.304336i	0.764698	−	0.644389i	$-0.222888\pi$
$211$	−7822.71	−	13549.3i	−0.175708	−	0.304336i	−0.940406	+	0.340053i	$0.889555\pi$
$212$	−61489.1	+	23884.8i	−1.36813	+	0.531434i
$213$		0			0
$214$	−28427.7	−	19454.6i	−0.620746	−	0.424810i
$215$		−	3975.76i		−	0.0860089i
$216$		0			0
$217$	−18541.0			−0.393743
$218$	−44636.7	+	65224.6i	−0.939245	+	1.37246i
$219$		0			0
$220$	−2370.70	+	920.873i	−0.0489814	+	0.0190263i
$221$	−15490.5	+	8943.44i	−0.317162	+	0.183113i
$222$		0			0
$223$	−44835.1	−	25885.6i	−0.901589	−	0.520532i	−0.0238733	−	0.999715i	$-0.507600\pi$
$223$	−44835.1	−	25885.6i	−0.901589	−	0.520532i	−0.877715	+	0.479183i	$0.840933\pi$
$224$	43701.7	+	17594.3i	0.870968	+	0.350652i
$225$		0			0
$226$	−5019.10	+	65438.9i	−0.0982674	+	1.28121i
$227$	28229.2	−	48894.4i	0.547831	−	0.948871i	−0.450592	−	0.892730i	$-0.648787\pi$
$227$	28229.2	−	48894.4i	0.547831	−	0.948871i	0.998423	−	0.0561410i	$-0.0178797\pi$
$228$		0			0
$229$	−48956.6	+	28265.1i	−0.933556	+	0.538989i	−0.887935	−	0.459970i	$-0.847860\pi$
$229$	−48956.6	+	28265.1i	−0.933556	+	0.538989i	−0.0456218	+	0.998959i	$0.514527\pi$
$230$	−2616.43	+	1254.37i	−0.0494599	+	0.0237121i
$231$		0			0
$232$	949.038	−	1012.11i	0.0176322	−	0.0188041i
$233$	−72322.4			−1.33217			−0.666087	−	0.745874i	$-0.732032\pi$
$233$	−72322.4			−1.33217			−0.666087	+	0.745874i	$0.732032\pi$
$234$		0			0
$235$	−10558.6			−0.191192
$236$	−52978.4	+	65958.1i	−0.951207	+	1.18425i
$237$		0			0
$238$	−7057.72	−	14721.3i	−0.124598	−	0.259892i
$239$	−86456.7	+	49915.8i	−1.51357	+	0.873861i	−0.513698	+	0.857971i	$0.671725\pi$
$239$	−86456.7	+	49915.8i	−1.51357	+	0.873861i	−0.999874	+	0.0158894i	$0.994942\pi$
$240$		0			0
$241$	−13108.7	+	22704.9i	−0.225697	+	0.390918i	−0.956528	−	0.291640i	$-0.905799\pi$
$241$	−13108.7	+	22704.9i	−0.225697	+	0.390918i	0.730832	+	0.682558i	$0.239132\pi$
$242$	−3578.55	+	46657.0i	−0.0611049	+	0.796684i
$243$		0			0
$244$	13462.7	−	87246.6i	0.226127	−	1.46544i
$245$	−721.778	−	416.719i	−0.0120246	−	0.00694242i
$246$		0			0
$247$	62350.4	−	35998.0i	1.02199	−	0.590045i
$248$	7473.04	+	24686.2i	0.121505	+	0.401376i
$249$		0			0
$250$	−8217.86	+	12008.2i	−0.131486	+	0.192131i
$251$	−110168.			−1.74866			−0.874332	−	0.485328i	$-0.838700\pi$
$251$	−110168.			−1.74866			−0.874332	+	0.485328i	$0.838700\pi$
$252$		0			0
$253$		−	13428.2i		−	0.209786i
$254$	−430.129	+	628.518i	−0.00666701	+	0.00974205i
$255$		0			0
$256$	5811.62	−	65277.8i	0.0886783	−	0.996060i
$257$	−21395.2	−	37057.7i	−0.323930	−	0.561063i	0.657365	−	0.753572i	$-0.271671\pi$
$257$	−21395.2	−	37057.7i	−0.323930	−	0.561063i	−0.981295	+	0.192509i	$0.938338\pi$
$258$		0			0
$259$	−29061.4	+	50335.8i	−0.433229	+	0.750374i
$260$	−9342.54	−	1441.61i	−0.138203	−	0.0213256i
$261$		0			0
$262$	−3266.76	+	42591.9i	−0.0475898	+	0.620475i
$263$	−70761.8	−	40854.3i	−1.02303	−	0.590645i	−0.108048	−	0.994146i	$-0.534460\pi$
$263$	−70761.8	−	40854.3i	−1.02303	−	0.590645i	−0.914979	+	0.403501i	$0.867793\pi$
$264$		0			0
$265$	6040.58	+	10462.6i	0.0860175	+	0.148987i
$266$	28407.9	+	59254.5i	0.401491	+	0.837448i
$267$		0			0
$268$	−61934.4	+	77108.3i	−0.862307	+	1.07357i
$269$			71867.3i			0.993177i	0.867986	+	0.496589i	$0.165414\pi$
$269$			71867.3i			0.993177i	−0.867986	+	0.496589i	$0.834586\pi$
$270$		0			0
$271$			57719.4i			0.785929i	0.919554	+	0.392964i	$0.128550\pi$
$271$			57719.4i			0.785929i	−0.919554	+	0.392964i	$0.871450\pi$
$272$	−16756.0	+	15330.5i	−0.226481	+	0.207213i
$273$		0			0
$274$	19289.4	−	9247.76i	0.256932	−	0.123179i
$275$	−16718.6	−	28957.5i	−0.221072	−	0.382909i
$276$		0			0
$277$	−17169.2	−	9912.65i	−0.223764	−	0.129190i	0.383928	−	0.923363i	$-0.374571\pi$
$277$	−17169.2	−	9912.65i	−0.223764	−	0.129190i	−0.607692	+	0.794173i	$0.707905\pi$
$278$	2545.17	−	33183.8i	0.0329327	−	0.429375i
$279$		0			0
$280$	1964.04	−	8401.53i	0.0250515	−	0.107162i
$281$	62271.1	−	107857.i	0.788631	−	1.36595i	−0.138175	−	0.990408i	$-0.544124\pi$
$281$	62271.1	−	107857.i	0.788631	−	1.36595i	0.926806	−	0.375541i	$-0.122543\pi$
$282$		0			0
$283$	−28575.7	−	49494.6i	−0.356799	−	0.617995i	0.630625	−	0.776088i	$-0.282799\pi$
$283$	−28575.7	−	49494.6i	−0.356799	−	0.617995i	−0.987424	+	0.158093i	$0.949465\pi$
$284$	72070.6	−	27995.0i	0.893555	−	0.347092i
$285$		0			0
$286$	24707.3	−	36103.1i	0.302060	−	0.441380i
$287$		−	101804.i		−	1.23595i
$288$		0			0
$289$	−75650.7			−0.905769
$290$	−209.702	−	143.510i	−0.00249348	−	0.00170642i
$291$		0			0
$292$	54662.1	+	140722.i	0.641092	+	1.65043i
$293$	25459.0	−	14698.8i	0.296555	−	0.171216i	−0.344339	−	0.938845i	$-0.611897\pi$
$293$	25459.0	−	14698.8i	0.296555	−	0.171216i	0.640894	+	0.767629i	$0.278564\pi$
$294$		0			0
$295$	13418.3	+	7747.04i	0.154189	+	0.0890209i
$296$	78732.7	+	18405.5i	0.898611	+	0.210070i
$297$		0			0
$298$	37911.2	+	2907.76i	0.426909	+	0.0327435i
$299$	24955.7	−	43224.5i	0.279143	−	0.483490i
$300$		0			0
$301$	−54057.2	+	31210.0i	−0.596652	+	0.344477i
$302$	−45992.4	−	95933.2i	−0.504281	−	1.05185i
$303$		0			0
$304$	67444.1	−	61706.3i	0.729788	−	0.667702i
$305$	−16167.9			−0.173801
$306$		0			0
$307$	−77280.8			−0.819964			−0.409982	−	0.912094i	$-0.634465\pi$
$307$	−77280.8			−0.819964			−0.409982	+	0.912094i	$0.634465\pi$
$308$	31131.0	+	25004.8i	0.328164	+	0.263586i
$309$		0			0
$310$	4259.55	−	2042.12i	0.0443242	−	0.0212500i
$311$	88843.4	−	51293.7i	0.918553	−	0.530327i	0.0353799	−	0.999374i	$-0.488736\pi$
$311$	88843.4	−	51293.7i	0.918553	−	0.530327i	0.883173	+	0.469047i	$0.155403\pi$
$312$		0			0
$313$	20566.6	−	35622.4i	0.209930	−	0.363609i	−0.741762	−	0.670663i	$-0.766010\pi$
$313$	20566.6	−	35622.4i	0.209930	−	0.363609i	0.951692	+	0.307054i	$0.0993431\pi$
$314$	−65658.5	−	5035.94i	−0.665934	−	0.0510766i
$315$		0			0
$316$	3098.84	−	20082.4i	0.0310331	−	0.201114i
$317$	109026.	+	62945.9i	1.08495	+	0.626396i	0.932227	−	0.361873i	$-0.117863\pi$
$317$	109026.	+	62945.9i	1.08495	+	0.626396i	0.152723	+	0.988269i	$0.451196\pi$
$318$		0			0
$319$	1018.43	−	587.989i	0.0100080	−	0.00577813i
$320$	−11977.8	+	771.277i	−0.116970	+	0.00753200i
$321$		0			0
$322$	37594.4	+	25727.9i	0.362587	+	0.248138i
$323$	−31678.5			−0.303640
$324$		0			0
$325$		−	124283.i		−	1.17664i
$326$	−22000.1	−	15055.8i	−0.207009	−	0.141667i
$327$		0			0
$328$	−135547.	+	41032.8i	−1.25991	+	0.381402i
$329$	82885.4	+	143562.i	0.765748	+	1.32632i
$330$		0			0
$331$	54232.0	−	93932.5i	0.494993	−	0.857354i	−0.504990	−	0.863125i	$-0.668504\pi$
$331$	54232.0	−	93932.5i	0.494993	−	0.857354i	0.999983	+	0.00577154i	$0.00183715\pi$
$332$	−40062.0	−	6181.80i	−0.363460	−	0.0560840i
$333$		0			0
$334$	88403.2	+	6780.44i	0.792455	+	0.0607806i
$335$	15686.6	+	9056.67i	0.139778	+	0.0807010i
$336$		0			0
$337$	−1823.71	−	3158.77i	−0.0160582	−	0.0278136i	0.857885	−	0.513842i	$-0.171778\pi$
$337$	−1823.71	−	3158.77i	−0.0160582	−	0.0278136i	−0.873943	+	0.486029i	$0.838445\pi$
$338$	43610.3	−	20907.7i	0.381730	−	0.183009i
$339$		0			0
$340$	3242.85	+	2604.70i	0.0280523	+	0.0225320i
$341$			21861.1i			0.188003i
$342$		0			0
$343$			123546.i			1.05013i
$344$	63342.4	+	59394.8i	0.535276	+	0.501917i
$345$		0			0
$346$	19387.8	+	40439.9i	0.161948	+	0.337799i
$347$	86264.4	+	149414.i	0.716428	+	1.24089i	0.962406	+	0.271615i	$0.0875576\pi$
$347$	86264.4	+	149414.i	0.716428	+	1.24089i	−0.245978	+	0.969275i	$0.579109\pi$
$348$		0			0
$349$	138147.	+	79759.0i	1.13420	+	0.654831i	0.944988	−	0.327106i	$-0.106073\pi$
$349$	138147.	+	79759.0i	1.13420	+	0.654831i	0.189212	+	0.981936i	$0.439407\pi$
$350$	113103.	+	8674.93i	0.923293	+	0.0708157i
$351$		0			0
$352$	20745.0	−	51527.5i	0.167428	−	0.415866i
$353$	20555.4	−	35603.0i	0.164959	−	0.285718i	−0.771681	−	0.636009i	$-0.780584\pi$
$353$	20555.4	−	35603.0i	0.164959	−	0.285718i	0.936641	+	0.350291i	$0.113917\pi$
$354$		0			0
$355$	−7080.09	−	12263.1i	−0.0561800	−	0.0973067i
$356$	−34222.6	−	88103.0i	−0.270031	−	0.695170i
$357$		0			0
$358$	56075.8	+	38375.7i	0.437532	+	0.299427i
$359$			76360.8i			0.592491i	0.955112	+	0.296245i	$0.0957346\pi$
$359$			76360.8i			0.592491i	−0.955112	+	0.296245i	$0.904265\pi$
$360$		0			0
$361$	−2812.82			−0.0215838
$362$	−109552.	+	160082.i	−0.835997	+	1.22159i
$363$		0			0
$364$	53738.3	+	138344.i	0.405584	+	1.04414i
$365$	23944.4	−	13824.3i	0.179729	−	0.103767i
$366$		0			0
$367$	102925.	+	59423.6i	0.764165	+	0.441191i	0.830789	−	0.556587i	$-0.187889\pi$
$367$	102925.	+	59423.6i	0.764165	+	0.441191i	−0.0666239	+	0.997778i	$0.521223\pi$
$368$	19102.6	−	60424.7i	0.141058	−	0.446189i
$369$		0			0
$370$	1132.45	−	14764.9i	0.00827212	−	0.107852i
$371$	94837.8	−	164264.i	0.689023	−	1.19342i
$372$		0			0
$373$	−115434.	+	66645.9i	−0.829691	+	0.479023i	−0.853747	−	0.520688i	$-0.825675\pi$
$373$	−115434.	+	66645.9i	−0.829691	+	0.479023i	0.0240556	+	0.999711i	$0.492342\pi$
$374$	−17357.5	+	8321.57i	−0.124092	+	0.0594925i
$375$		0			0
$376$	157737.	−	168221.i	1.11573	−	1.18988i
$377$	4371.00			0.0307537
$378$		0			0
$379$	141694.			0.986447			0.493224	−	0.869902i	$-0.335818\pi$
$379$	141694.			0.986447			0.493224	+	0.869902i	$0.335818\pi$
$380$	−13052.7	−	10484.1i	−0.0903927	−	0.0726047i
$381$		0			0
$382$	−63148.8	−	131719.i	−0.432751	−	0.902653i
$383$	43983.8	−	25394.1i	0.299844	−	0.173115i	−0.342529	−	0.939507i	$-0.611283\pi$
$383$	43983.8	−	25394.1i	0.299844	−	0.173115i	0.642373	+	0.766392i	$0.277950\pi$
$384$		0			0
$385$	3656.46	−	6333.17i	0.0246683	−	0.0427267i
$386$	7682.86	−	100169.i	0.0515642	−	0.672292i
$387$		0			0
$388$	−29380.2	−	4533.54i	−0.195160	−	0.0301144i
$389$	−103180.	−	59570.8i	−0.681860	−	0.393672i	0.118696	−	0.992931i	$-0.462129\pi$
$389$	−103180.	−	59570.8i	−0.681860	−	0.393672i	−0.800555	+	0.599259i	$0.795462\pi$
$390$		0			0
$391$	−19018.9	+	10980.6i	−0.124403	+	0.0718242i
$392$	17422.0	−	5274.01i	0.113377	−	0.0343217i
$393$		0			0
$394$	−64472.8	+	94209.7i	−0.415321	+	0.606881i
$395$	−3721.53			−0.0238521
$396$		0			0
$397$		−	200049.i		−	1.26927i	−0.772812	−	0.634635i	$-0.781150\pi$
$397$		−	200049.i		−	1.26927i	0.772812	−	0.634635i	$-0.218850\pi$
$398$	144386.	−	210981.i	0.911504	−	1.33192i
$399$		0			0
$400$	−34036.8	−	154087.i	−0.212730	−	0.963046i
$401$	13977.6	+	24209.9i	0.0869248	+	0.150558i	0.906210	−	0.422828i	$-0.138963\pi$
$401$	13977.6	+	24209.9i	0.0869248	+	0.150558i	−0.819285	+	0.573387i	$0.805629\pi$
$402$		0			0
$403$	−40627.9	+	70369.6i	−0.250158	+	0.433286i
$404$	−38999.1	+	252739.i	−0.238941	+	1.54849i
$405$		0			0
$406$	−305.095	+	3977.82i	−0.00185090	+	0.0241320i
$407$	59349.6	+	34265.5i	0.358285	+	0.206856i
$408$		0			0
$409$	−27650.2	−	47891.6i	−0.165292	−	0.286294i	0.771467	−	0.636270i	$-0.219523\pi$
$409$	−27650.2	−	47891.6i	−0.165292	−	0.286294i	−0.936759	+	0.349975i	$0.886190\pi$
$410$	11212.8	+	23388.3i	0.0667033	+	0.139133i
$411$		0			0
$412$	246227.	+	197773.i	1.45058	+	1.16513i
$413$		−	243259.i		−	1.42616i
$414$		0			0
$415$			7423.98i			0.0431063i
$416$	162538.	−	127310.i	0.939223	−	0.735658i
$417$		0			0
$418$	69865.4	−	33494.9i	0.399861	−	0.191702i
$419$	76753.4	+	132941.i	0.437189	+	0.757234i	0.997472	−	0.0710675i	$-0.0226406\pi$
$419$	76753.4	+	132941.i	0.437189	+	0.757234i	−0.560282	+	0.828302i	$0.689307\pi$
$420$		0			0
$421$	230275.	+	132949.i	1.29922	+	0.750105i	0.980269	−	0.197667i	$-0.0633364\pi$
$421$	230275.	+	132949.i	1.29922	+	0.750105i	0.318950	+	0.947771i	$0.396670\pi$
$422$	4785.90	−	62398.4i	0.0268744	−	0.350387i
$423$		0			0
$424$	−256933.	−	60063.7i	−1.42918	−	0.334103i
$425$	−27342.4	+	47358.5i	−0.151377	+	0.262192i
$426$		0			0
$427$	126919.	+	219830.i	0.696097	+	1.20568i
$428$	−49890.9	−	128440.i	−0.272354	−	0.701150i
$429$		0			0
$430$	8981.48	−	13124.0i	0.0485748	−	0.0709790i
$431$			187074.i			1.00707i	0.863976	+	0.503533i	$0.167967\pi$
$431$			187074.i			1.00707i	−0.863976	+	0.503533i	$0.832033\pi$
$432$		0			0
$433$	252526.			1.34688			0.673441	−	0.739241i	$-0.264815\pi$
$433$	252526.			1.34688			0.673441	+	0.739241i	$0.264815\pi$
$434$	−61203.8	−	41885.1i	−0.324937	−	0.222372i
$435$		0			0
$436$	−294692.	+	114470.i	−1.55023	+	0.602169i
$437$	76552.5	−	44197.6i	0.400863	−	0.231439i
$438$		0			0
$439$	−138415.	−	79914.0i	−0.718215	−	0.414662i	0.0958801	−	0.995393i	$-0.469433\pi$
$439$	−138415.	−	79914.0i	−0.718215	−	0.414662i	−0.814095	+	0.580731i	$0.802767\pi$
$440$	−9906.01	−	2315.75i	−0.0511674	−	0.0119615i
$441$		0			0
$442$	−71338.0	−	5471.56i	−0.365154	−	0.0280070i
$443$	−152813.	+	264680.i	−0.778670	+	1.34870i	0.154038	+	0.988065i	$0.450772\pi$
$443$	−152813.	+	264680.i	−0.778670	+	1.34870i	−0.932708	+	0.360632i	$0.882561\pi$
$444$		0			0
$445$	−14991.1	+	8655.09i	−0.0757028	+	0.0437070i
$446$	−89524.0	−	186734.i	−0.450060	−	0.938756i
$447$		0			0
$448$	104513.	+	156804.i	0.520732	+	0.781268i
$449$	−338152.			−1.67733			−0.838667	−	0.544645i	$-0.816664\pi$
$449$	−338152.			−1.67733			−0.838667	+	0.544645i	$0.816664\pi$
$450$		0			0
$451$	−120035.			−0.590138
$452$	−164398.	+	204676.i	−0.804675	+	1.00182i
$453$		0			0
$454$	203640.	−	97629.4i	0.987987	−	0.473662i
$455$	23539.8	−	13590.7i	0.113705	−	0.0656477i
$456$		0			0
$457$	−1641.07	+	2842.42i	−0.00785770	+	0.0136099i	−0.869928	−	0.493180i	$-0.835835\pi$
$457$	−1641.07	+	2842.42i	−0.00785770	+	0.0136099i	0.862070	+	0.506790i	$0.169168\pi$
$458$	−225459.	−	17292.5i	−1.07482	−	0.0824378i
$459$		0			0
$460$	−11470.6	−	1769.97i	−0.0542087	−	0.00836472i
$461$	−215070.	−	124171.i	−1.01199	−	0.584275i	−0.100220	−	0.994965i	$-0.531955\pi$
$461$	−215070.	−	124171.i	−1.01199	−	0.584275i	−0.911775	+	0.410690i	$0.865288\pi$
$462$		0			0
$463$	−42958.9	+	24802.3i	−0.200397	+	0.115699i	−0.596841	−	0.802360i	$-0.703578\pi$
$463$	−42958.9	+	24802.3i	−0.200397	+	0.115699i	0.396444	+	0.918059i	$0.370244\pi$
$464$	5419.21	−	1197.07i	0.0251710	−	0.00556009i
$465$		0			0
$466$	−238737.	−	163380.i	−1.09938	−	0.752365i
$467$	−18727.6			−0.0858712			−0.0429356	−	0.999078i	$-0.513671\pi$
$467$	−18727.6			−0.0858712			−0.0429356	+	0.999078i	$0.513671\pi$
$468$		0			0
$469$		−	284381.i		−	1.29287i
$470$	−34853.9	−	23852.4i	−0.157782	−	0.107978i
$471$		0			0
$472$	−323886.	+	98046.9i	−1.45381	+	0.440099i
$473$	36798.8	+	63737.4i	0.164479	+	0.284887i
$474$		0			0
$475$	110055.	−	190621.i	0.487780	−	0.844859i
$476$	9958.76	−	64539.1i	0.0439533	−	0.284845i
$477$		0			0
$478$	−398157.	−	30538.3i	−1.74260	−	0.133656i
$479$	343234.	+	198166.i	1.49596	+	0.863691i	0.999989	−	0.00465021i	$-0.00148021\pi$
$479$	343234.	+	198166.i	1.49596	+	0.863691i	0.495967	+	0.868341i	$0.334814\pi$
$480$		0			0
$481$	127362.	+	220597.i	0.550489	+	0.953475i
$482$	−94563.6	+	45335.8i	−0.407033	+	0.195140i
$483$		0			0
$484$	−117214.	+	145931.i	−0.500366	+	0.622955i
$485$			5444.52i			0.0231460i
$486$		0			0
$487$			240262.i			1.01304i	0.862228	+	0.506520i	$0.169068\pi$
$487$			240262.i			1.01304i	−0.862228	+	0.506520i	$0.830932\pi$
$488$	241536.	−	257589.i	1.01424	−	1.08165i
$489$		0			0
$490$	−1441.20	−	3006.13i	−0.00600251	−	0.0125203i
$491$	−98040.3	−	169811.i	−0.406670	−	0.704372i	0.587845	−	0.808974i	$-0.299977\pi$
$491$	−98040.3	−	169811.i	−0.406670	−	0.704372i	−0.994514	+	0.104601i	$0.966643\pi$
$492$		0			0
$493$	−1665.58	−	961.625i	−0.00685287	−	0.00395651i
$494$	287141.	+	22023.4i	1.17663	+	0.0902467i
$495$		0			0
$496$	−31099.1	+	98371.5i	−0.126411	+	0.399858i
$497$	−111158.	+	192532.i	−0.450017	+	0.779452i
$498$		0			0
$499$	130948.	+	226808.i	0.525892	+	0.910871i	0.999545	+	0.0301596i	$0.00960157\pi$
$499$	130948.	+	226808.i	0.525892	+	0.910871i	−0.473654	+	0.880711i	$0.657065\pi$
$500$	−54254.4	+	21074.5i	−0.217018	+	0.0842981i
$501$		0			0
$502$	−363664.	−	248875.i	−1.44309	−	0.987583i
$503$			311251.i			1.23020i	0.788450	+	0.615099i	$0.210884\pi$
$503$			311251.i			1.23020i	−0.788450	+	0.615099i	$0.789116\pi$
$504$		0			0
$505$	46835.6			0.183651
$506$	30335.1	−	44326.6i	0.118480	−	0.173126i
$507$		0			0
$508$	−2839.72	+	1103.06i	−0.0110039	+	0.00427435i
$509$	−317446.	+	183278.i	−1.22528	+	0.707415i	−0.966039	−	0.258398i	$-0.916805\pi$
$509$	−317446.	+	183278.i	−1.22528	+	0.707415i	−0.259240	+	0.965813i	$0.583472\pi$
$510$		0			0
$511$	−375930.	−	217043.i	−1.43968	−	0.831199i
$512$	166651.	−	202354.i	0.635722	−	0.771918i
$513$		0			0
$514$	13089.5	−	170661.i	0.0495447	−	0.645963i
$515$	28920.4	−	50091.6i	0.109041	−	0.188864i
$516$		0			0
$517$	169270.	−	97727.9i	0.633283	−	0.365626i
$518$	−209644.	+	100508.i	−0.781307	+	0.374575i
$519$		0			0
$520$	−27583.1	−	25864.1i	−0.102009	−	0.0956512i
$521$	526988.			1.94145			0.970723	−	0.240203i	$-0.0772142\pi$
$521$	526988.			1.94145			0.970723	+	0.240203i	$0.0772142\pi$
$522$		0			0
$523$	311012.			1.13703			0.568517	−	0.822671i	$-0.307517\pi$
$523$	311012.			1.13703			0.568517	+	0.822671i	$0.307517\pi$
$524$	−107001.	+	133216.i	−0.389696	+	0.485171i
$525$		0			0
$526$	−141293.	−	294715.i	−0.510680	−	1.06520i
$527$	30962.8	−	17876.4i	0.111486	−	0.0643663i
$528$		0			0
$529$	−109280.	+	189279.i	−0.390509	+	0.676382i
$530$	−3695.60	+	48183.1i	−0.0131563	+	0.171531i
$531$		0			0
$532$	−40084.8	+	259775.i	−0.141630	+	0.917854i
$533$	−386384.	−	223079.i	−1.36008	−	0.785242i
$534$		0			0
$535$	−21854.5	+	12617.7i	−0.0763541	+	0.0440831i
$536$	−378638.	+	114622.i	−1.31794	+	0.398967i
$537$		0			0
$538$	−162352.	+	237235.i	−0.560911	+	0.819622i
$539$	15428.2			0.0531054
$540$		0			0
$541$		−	377631.i		−	1.29025i	−0.764078	−	0.645124i	$-0.776806\pi$
$541$		−	377631.i		−	1.29025i	0.764078	−	0.645124i	$-0.223194\pi$
$542$	−130391.	+	190532.i	−0.443865	+	0.648589i
$543$		0			0
$544$	−89944.1	+	12753.3i	−0.303931	+	0.0430949i
$545$	28950.0	+	50143.0i	0.0974667	+	0.168817i
$546$		0			0
$547$	−51766.7	+	89662.5i	−0.173012	+	0.299665i	−0.939471	−	0.342627i	$-0.888683\pi$
$547$	−51766.7	+	89662.5i	−0.173012	+	0.299665i	0.766460	+	0.642292i	$0.222017\pi$
$548$	84565.8	+	13049.0i	0.281601	+	0.0434526i
$549$		0			0
$550$	10228.4	−	133357.i	0.0338128	−	0.440850i
$551$	6704.10	+	3870.61i	0.0220819	+	0.0127490i
$552$		0			0
$553$	29214.2	+	50600.4i	0.0955308	+	0.165464i
$554$	−34282.5	−	71508.0i	−0.111700	−	0.232989i
$555$		0			0
$556$	83365.8	−	103790.i	0.269674	−	0.335744i
$557$		−	321643.i		−	1.03673i	−0.855161	−	0.518363i	$-0.826542\pi$
$557$		−	321643.i		−	1.03673i	0.855161	−	0.518363i	$-0.173458\pi$
$558$		0			0
$559$			273556.i			0.875431i
$560$	25462.8	−	23296.6i	0.0811953	−	0.0742877i
$561$		0			0
$562$	449212.	−	215362.i	1.42226	−	0.681861i
$563$	15717.8	+	27224.0i	0.0495878	+	0.0858885i	0.889754	−	0.456441i	$-0.150876\pi$
$563$	15717.8	+	27224.0i	0.0495878	+	0.0858885i	−0.840166	+	0.542329i	$0.817543\pi$
$564$		0			0
$565$	41638.5	+	24040.0i	0.130436	+	0.0753074i
$566$	17482.5	−	227936.i	0.0545721	−	0.711509i
$567$		0			0
$568$	301148.	+	70399.9i	0.933433	+	0.218210i
$569$	−118855.	+	205862.i	−0.367106	+	0.635846i	−0.989112	−	0.147166i	$-0.952985\pi$
$569$	−118855.	+	205862.i	−0.367106	+	0.635846i	0.622006	+	0.783013i	$0.286318\pi$
$570$		0			0
$571$	−259870.	−	450108.i	−0.797047	−	1.38053i	−0.921531	−	0.388304i	$-0.873061\pi$
$571$	−259870.	−	450108.i	−0.797047	−	1.38053i	0.124484	−	0.992222i	$-0.460272\pi$
$572$	163118.	−	63361.4i	0.498551	−	0.193657i
$573$		0			0
$574$	229982.	−	336057.i	0.698023	−	1.01997i
$575$		−	152592.i		−	0.461526i
$576$		0			0
$577$	−150655.			−0.452513			−0.226257	−	0.974068i	$-0.572649\pi$
$577$	−150655.			−0.452513			−0.226257	+	0.974068i	$0.572649\pi$
$578$	−249724.	−	170899.i	−0.747488	−	0.511546i
$579$		0			0
$580$	−368.029	−	947.457i	−0.00109402	−	0.00281646i
$581$	100942.	−	58278.7i	0.299032	−	0.172646i
$582$		0			0
$583$	−193679.	−	111821.i	−0.569830	−	0.328992i
$584$	−137460.	+	588011.i	−0.403043	+	1.72409i
$585$		0			0
$586$	117246.	+	8992.64i	0.341430	+	0.0261874i
$587$	−222883.	+	386045.i	−0.646846	+	1.12037i	0.337025	+	0.941496i	$0.390579\pi$
$587$	−222883.	+	386045.i	−0.646846	+	1.12037i	−0.983872	+	0.178875i	$0.942754\pi$
$588$		0			0
$589$	−124628.	+	71953.8i	−0.359239	+	0.207407i
$590$	26792.8	+	55885.7i	0.0769687	+	0.160545i
$591$		0			0
$592$	218318.	+	238618.i	0.622941	+	0.680864i
$593$	59064.6			0.167965			0.0839823	−	0.996467i	$-0.473236\pi$
$593$	59064.6			0.167965			0.0839823	+	0.996467i	$0.473236\pi$
$594$		0			0
$595$	−11959.9			−0.0337826
$596$	118577.	+	95242.3i	0.333815	+	0.268125i
$597$		0			0
$598$	180026.	−	86308.1i	0.503422	−	0.241351i
$599$	−354748.	+	204814.i	−0.988703	+	0.570828i	−0.904886	−	0.425653i	$-0.860044\pi$
$599$	−354748.	+	204814.i	−0.988703	+	0.570828i	−0.0838164	+	0.996481i	$0.526711\pi$
$600$		0			0
$601$	268772.	−	465527.i	0.744107	−	1.28883i	−0.206505	−	0.978446i	$-0.566209\pi$
$601$	268772.	−	465527.i	0.744107	−	1.28883i	0.950611	−	0.310385i	$-0.100458\pi$
$602$	−248948.	−	19094.1i	−0.686936	−	0.0526874i
$603$		0			0
$604$	64897.3	−	420576.i	0.177891	−	1.15284i
$605$	29687.6	+	17140.2i	0.0811082	+	0.0468279i
$606$		0			0
$607$	377551.	−	217979.i	1.02470	−	0.591614i	0.109242	−	0.994015i	$-0.465158\pi$
$607$	377551.	−	217979.i	1.02470	−	0.591614i	0.915463	+	0.402402i	$0.131824\pi$
$608$	362032.	−	51333.1i	0.979353	−	0.138864i
$609$		0			0
$610$	−53370.3	−	36524.2i	−0.143430	−	0.0981569i
$611$	726491.			1.94602
$612$		0			0
$613$		−	184751.i		−	0.491662i	−0.969313	−	0.245831i	$-0.920939\pi$
$613$		−	184751.i		−	0.491662i	0.969313	−	0.245831i	$-0.0790608\pi$
$614$	−255105.	−	174582.i	−0.676677	−	0.463087i
$615$		0			0
$616$	46276.3	+	152868.i	0.121954	+	0.402860i
$617$	−70628.6	−	122332.i	−0.185528	−	0.321344i	0.758226	−	0.651992i	$-0.226066\pi$
$617$	−70628.6	−	122332.i	−0.185528	−	0.321344i	−0.943754	+	0.330647i	$0.892733\pi$
$618$		0			0
$619$	−132429.	+	229374.i	−0.345623	+	0.598637i	−0.985467	−	0.169868i	$-0.945666\pi$
$619$	−132429.	+	229374.i	−0.345623	+	0.598637i	0.639844	+	0.768505i	$0.278999\pi$
$620$	18674.1	+	2881.52i	0.0485799	+	0.00749616i
$621$		0			0
$622$	409148.	+	31381.3i	1.05755	+	0.0811129i
$623$	235361.	+	135886.i	0.606399	+	0.350105i
$624$		0			0
$625$	−187299.	−	324412.i	−0.479486	−	0.830494i
$626$	148364.	−	71128.7i	0.378599	−	0.181508i
$627$		0			0
$628$	−205363.	−	164950.i	−0.520717	−	0.418247i
$629$		−	112079.i		−	0.283285i
$630$		0			0
$631$			699879.i			1.75778i	0.477026	+	0.878889i	$0.341715\pi$
$631$			699879.i			1.75778i	−0.477026	+	0.878889i	$0.658285\pi$
$632$	55596.7	−	59291.8i	0.139192	−	0.148443i
$633$		0			0
$634$	217696.	+	454080.i	0.541591	+	1.12968i
$635$	278.969	+	483.188i	0.000691844	+	0.00119831i
$636$		0			0
$637$	49662.5	+	28672.7i	0.122391	+	0.0706625i
$638$	4690.13	+	359.729i	0.0115224	+	0.000883759i
$639$		0			0
$640$	−41281.1	−	24512.5i	−0.100784	−	0.0598450i
$641$	159686.	−	276584.i	0.388643	−	0.673149i	−0.603625	−	0.797269i	$-0.706277\pi$
$641$	159686.	−	276584.i	0.388643	−	0.673149i	0.992267	+	0.124120i	$0.0396107\pi$
$642$		0			0
$643$	−120033.	−	207903.i	−0.290321	−	0.502850i	0.683565	−	0.729890i	$-0.260429\pi$
$643$	−120033.	−	207903.i	−0.290321	−	0.502850i	−0.973886	+	0.227040i	$0.927095\pi$
$644$	65978.7	+	169856.i	0.159086	+	0.409552i
$645$		0			0
$646$	−104571.	−	71563.5i	−0.250580	−	0.171485i
$647$		−	160526.i		−	0.383475i	−0.981446	−	0.191737i	$-0.938588\pi$
$647$		−	160526.i		−	0.383475i	0.981446	−	0.191737i	$-0.0614122\pi$
$648$		0			0
$649$	−286820.			−0.680957
$650$	280763.	−	410259.i	0.664527	−	0.971028i
$651$		0			0
$652$	−38610.4	−	99399.0i	−0.0908258	−	0.233823i
$653$	23755.5	−	13715.3i	0.0557107	−	0.0321646i	−0.471886	−	0.881660i	$-0.656427\pi$
$653$	23755.5	−	13715.3i	0.0557107	−	0.0321646i	0.527597	+	0.849495i	$0.323093\pi$
$654$		0			0
$655$	27101.0	+	15646.8i	0.0631689	+	0.0364706i
$656$	−540136.	−	170758.i	−1.25515	−	0.396802i
$657$		0			0
$658$	−50708.9	+	661141.i	−0.117120	+	1.52701i
$659$	215117.	−	372594.i	0.495341	−	0.857957i	−0.504644	−	0.863327i	$-0.668376\pi$
$659$	215117.	−	372594.i	0.495341	−	0.857957i	0.999986	+	0.00537093i	$0.00170963\pi$
$660$		0			0
$661$	−122972.	+	70998.0i	−0.281451	+	0.162496i	−0.634080	−	0.773267i	$-0.718621\pi$
$661$	−122972.	+	70998.0i	−0.281451	+	0.162496i	0.352629	+	0.935763i	$0.385288\pi$
$662$	391219.	−	187559.i	0.892697	−	0.427978i
$663$		0			0
$664$	−118280.	−	110908.i	−0.268272	−	0.251552i
$665$	48139.5			0.108857
$666$		0			0
$667$	5366.61			0.0120628
$668$	276502.	+	222090.i	0.619649	+	0.497710i
$669$		0			0
$670$	31322.1	+	65333.1i	0.0697752	+	0.145540i
$671$	259195.	−	149646.i	0.575681	−	0.332370i
$672$		0			0
$673$	−78759.2	+	136415.i	−0.173889	+	0.301184i	−0.939776	−	0.341791i	$-0.888967\pi$
$673$	−78759.2	+	136415.i	−0.173889	+	0.301184i	0.765887	+	0.642975i	$0.222300\pi$
$674$	1115.74	−	14547.0i	0.00245609	−	0.0320224i
$675$		0			0
$676$	191190.	+	29501.7i	0.418380	+	0.0645585i
$677$	606737.	+	350300.i	1.32380	+	0.764298i	0.984333	−	0.176319i	$-0.0564190\pi$
$677$	606737.	+	350300.i	1.32380	+	0.764298i	0.339470	+	0.940617i	$0.389752\pi$
$678$		0			0
$679$	74027.5	−	42739.8i	0.160566	−	0.0927028i
$680$	4820.50	+	15923.9i	0.0104250	+	0.0344375i
$681$		0			0
$682$	−49385.6	+	72163.8i	−0.106177	+	0.155150i
$683$	−408773.			−0.876275			−0.438137	−	0.898908i	$-0.644362\pi$
$683$	−408773.			−0.876275			−0.438137	+	0.898908i	$0.644362\pi$
$684$		0			0
$685$		−	15671.1i		−	0.0333978i
$686$	−279098.	+	407827.i	−0.593074	+	0.866618i
$687$		0			0
$688$	74917.4	+	339157.i	0.158273	+	0.716512i
$689$	−415627.	−	719887.i	−0.875518	−	1.51644i
$690$		0			0
$691$	−309805.	+	536598.i	−0.648832	+	1.12381i	0.334570	+	0.942371i	$0.391409\pi$
$691$	−309805.	+	536598.i	−0.648832	+	1.12381i	−0.983402	+	0.181439i	$0.941924\pi$
$692$	−27357.0	+	177291.i	−0.0571289	+	0.370232i
$693$		0			0
$694$	−52776.2	+	688094.i	−0.109577	+	1.42866i
$695$	−21114.7	−	12190.6i	−0.0437135	−	0.0252380i
$696$		0			0
$697$	98155.2	+	170010.i	0.202045	+	0.349952i
$698$	275843.	+	575367.i	0.566176	+	1.18096i
$699$		0			0
$700$	353758.	+	284143.i	0.721955	+	0.579884i
$701$			98886.5i			0.201234i	0.994925	+	0.100617i	$0.0320816\pi$
$701$			98886.5i			0.201234i	−0.994925	+	0.100617i	$0.967918\pi$
$702$		0			0
$703$			451126.i			0.912825i
$704$	184883.	−	123228.i	0.373037	−	0.248637i
$705$		0			0
$706$	148283.	−	71090.0i	0.297496	−	0.142626i
$707$	−367662.	−	636809.i	−0.735546	−	1.27400i
$708$		0			0
$709$	16701.3	+	9642.51i	0.0332245	+	0.0191822i	0.516520	−	0.856275i	$-0.327227\pi$
$709$	16701.3	+	9642.51i	0.0332245	+	0.0191822i	−0.483296	+	0.875457i	$0.660560\pi$
$710$	4331.57	−	56474.9i	0.00859268	−	0.112031i
$711$		0			0
$712$	86060.7	−	368140.i	0.169764	−	0.726194i
$713$	−49882.0	+	86398.2i	−0.0981217	+	0.169952i
$714$		0			0
$715$	−16024.4	−	27755.1i	−0.0313452	−	0.0542914i
$716$	98413.7	+	253357.i	0.191968	+	0.494205i
$717$		0			0
$718$	−172503.	+	252068.i	−0.334618	+	0.488954i
$719$			124940.i			0.241681i	0.992672	+	0.120841i	$0.0385590\pi$
$719$			124940.i			0.241681i	−0.992672	+	0.120841i	$0.961441\pi$
$720$		0			0
$721$	−908107.			−1.74689
$722$	−9285.15	−	6354.33i	−0.0178121	−	0.0121898i
$723$		0			0
$724$	−723267.	+	280945.i	−1.37982	+	0.535975i
$725$	11572.9	−	6681.64i	0.0220175	−	0.0127118i
$726$		0			0
$727$	237638.	+	137200.i	0.449621	+	0.259589i	0.707670	−	0.706543i	$-0.249746\pi$
$727$	237638.	+	137200.i	0.449621	+	0.259589i	−0.258049	+	0.966132i	$0.583080\pi$
$728$	−135137.	+	578074.i	−0.254984	+	1.09074i
$729$		0			0
$730$	110271.	+	8457.67i	0.206926	+	0.0158710i
$731$	60182.6	−	104239.i	0.112625	−	0.195073i
$732$		0			0
$733$	−196395.	+	113389.i	−0.365530	+	0.211039i	−0.671504	−	0.741001i	$-0.734351\pi$
$733$	−196395.	+	113389.i	−0.365530	+	0.211039i	0.305974	+	0.952040i	$0.401018\pi$
$734$	205514.	+	428671.i	0.381460	+	0.795667i
$735$		0			0
$736$	199561.	−	156308.i	0.368400	−	0.288554i
$737$	−335306.			−0.617315
$738$		0			0
$739$	−173966.			−0.318549			−0.159274	−	0.987234i	$-0.550915\pi$
$739$	−173966.			−0.318549			−0.159274	+	0.987234i	$0.550915\pi$
$740$	37093.0	−	46180.7i	0.0677374	−	0.0843330i
$741$		0			0
$742$	684142.	−	327992.i	1.24262	−	0.595739i
$743$	223552.	−	129068.i	0.404949	−	0.233797i	−0.283668	−	0.958923i	$-0.591551\pi$
$743$	223552.	−	129068.i	0.404949	−	0.233797i	0.688617	+	0.725125i	$0.258218\pi$
$744$		0			0
$745$	13927.3	−	24122.8i	0.0250931	−	0.0434625i
$746$	−531606.	−	40773.7i	−0.955239	−	0.0732660i
$747$		0			0
$748$	−76096.3	−	11742.1i	−0.136007	−	0.0209866i
$749$	343117.	+	198099.i	0.611616	+	0.353117i
$750$		0			0
$751$	439854.	−	253950.i	0.779881	−	0.450264i	−0.0565073	−	0.998402i	$-0.517996\pi$
$751$	439854.	−	253950.i	0.779881	−	0.450264i	0.836388	+	0.548138i	$0.184663\pi$
$752$	900711.	−	198961.i	1.59276	−	0.351829i
$753$		0			0
$754$	14428.7	+	9874.34i	0.0253796	+	0.0173686i
$755$	−77937.9			−0.136727
$756$		0			0
$757$			146756.i			0.256097i	0.991768	+	0.128048i	$0.0408713\pi$
$757$			146756.i			0.256097i	−0.991768	+	0.128048i	$0.959129\pi$
$758$	467734.	+	320096.i	0.814068	+	0.557111i
$759$		0			0
$760$	−19402.9	−	64095.0i	−0.0335923	−	0.110968i
$761$	−106335.	−	184178.i	−0.183615	−	0.318030i	0.759494	−	0.650514i	$-0.225447\pi$
$761$	−106335.	−	184178.i	−0.183615	−	0.318030i	−0.943109	+	0.332484i	$0.892113\pi$
$762$		0			0
$763$	454519.	−	787250.i	0.780734	−	1.35227i
$764$	89105.7	−	577461.i	0.152658	−	0.989319i
$765$		0			0
$766$	202558.	+	15536.0i	0.345216	+	0.0264778i
$767$	−923255.	−	533042.i	−1.56939	−	0.906088i
$768$		0			0
$769$	44021.9	+	76248.2i	0.0744417	+	0.128937i	0.900843	−	0.434144i	$-0.142949\pi$
$769$	44021.9	+	76248.2i	0.0744417	+	0.128937i	−0.826402	+	0.563081i	$0.809616\pi$
$770$	26377.0	−	12645.7i	0.0444881	−	0.0213285i
$771$		0			0
$772$	251648.	−	313302.i	0.422240	−	0.525689i
$773$			956337.i			1.60049i	0.599675	+	0.800243i	$0.295296\pi$
$773$			956337.i			1.60049i	−0.599675	+	0.800243i	$0.704704\pi$
$774$		0			0
$775$			248420.i			0.413602i
$776$	−86742.9	−	81336.9i	−0.144049	−	0.135072i
$777$		0			0
$778$	−206023.	−	429733.i	−0.340374	−	0.709969i
$779$	−395082.	−	684302.i	−0.651047	−	1.12765i
$780$		0			0
$781$	227009.	+	131064.i	0.372169	+	0.214872i
$782$	−87587.2	−	6717.86i	−0.143228	−	0.0109854i
$783$		0			0
$784$	69424.5	+	21947.8i	0.112949	+	0.0357075i
$785$	−24120.7	+	41778.2i	−0.0391426	+	0.0677970i
$786$		0			0
$787$	−150134.	−	260040.i	−0.242398	−	0.419846i	0.718999	−	0.695012i	$-0.244601\pi$
$787$	−150134.	−	260040.i	−0.242398	−	0.419846i	−0.961397	+	0.275165i	$0.911267\pi$
$788$	−425650.	+	165339.i	−0.685489	+	0.266271i
$789$		0			0
$790$	−12284.8	−	8407.14i	−0.0196840	−	0.0134708i
$791$		−	754861.i		−	1.20646i
$792$		0			0
$793$	1.11244e6			1.76902
$794$	451921.	−	660362.i	0.716839	−	1.04747i
$795$		0			0
$796$	953238.	−	370275.i	1.50444	−	0.584383i
$797$	189436.	−	109371.i	0.298226	−	0.172181i	−0.343420	−	0.939182i	$-0.611585\pi$
$797$	189436.	−	109371.i	0.298226	−	0.172181i	0.641646	+	0.767001i	$0.278252\pi$
$798$		0			0
$799$	−276832.	−	159829.i	−0.433633	−	0.250358i
$800$	235736.	−	585535.i	0.368338	−	0.914898i
$801$		0			0
$802$	−8551.44	+	111493.i	−0.0132951	+	0.173341i
$803$	−255910.	+	443249.i	−0.396877	+	0.687412i
$804$		0			0
$805$	28901.6	−	16686.4i	0.0445996	−	0.0257496i
$806$	−293082.	+	140510.i	−0.451148	+	0.216290i
$807$		0			0
$808$	−699688.	+	746191.i	−1.07172	+	1.14295i
$809$	373854.			0.571223			0.285611	−	0.958346i	$-0.407803\pi$
$809$	373854.			0.571223			0.285611	+	0.958346i	$0.407803\pi$
$810$		0			0
$811$	−389516.			−0.592220			−0.296110	−	0.955154i	$-0.595690\pi$
$811$	−389516.			−0.592220			−0.296110	+	0.955154i	$0.595690\pi$
$812$	−9993.24	+	12441.6i	−0.0151563	+	0.0188696i
$813$		0			0
$814$	118506.	+	247185.i	0.178851	+	0.373055i
$815$	−16913.1	+	9764.78i	−0.0254629	+	0.0147010i
$816$		0			0
$817$	−242239.	+	419571.i	−0.362911	+	0.628581i
$818$	16916.3	−	220554.i	0.0252813	−	0.329616i
$819$		0			0
$820$	−15821.8	+	102535.i	−0.0235303	+	0.152492i
$821$	−766580.	−	442585.i	−1.13729	−	0.656614i	−0.191531	−	0.981486i	$-0.561345\pi$
$821$	−766580.	−	442585.i	−1.13729	−	0.656614i	−0.945758	+	0.324872i	$0.894679\pi$
$822$		0			0
$823$	556310.	−	321186.i	0.821329	−	0.474195i	−0.0295455	−	0.999563i	$-0.509406\pi$
$823$	556310.	−	321186.i	0.821329	−	0.474195i	0.850875	+	0.525369i	$0.176073\pi$
$824$	366018.	+	1.20909e6i	0.539073	+	1.78076i
$825$		0			0
$826$	549536.	−	803000.i	0.805445	−	1.17694i
$827$	144563.			0.211372			0.105686	−	0.994400i	$-0.466296\pi$
$827$	144563.			0.211372			0.105686	+	0.994400i	$0.466296\pi$
$828$		0			0
$829$			390583.i			0.568335i	0.958775	+	0.284167i	$0.0917171\pi$
$829$			390583.i			0.568335i	−0.958775	+	0.284167i	$0.908283\pi$
$830$	−16771.2	+	24506.6i	−0.0243449	+	0.0355735i
$831$		0			0
$832$	824140.	−	53068.3i	1.19057	−	0.0766635i
$833$	−12616.0	−	21851.6i	−0.0181816	−	0.0314915i
$834$		0			0
$835$	32476.3	−	56250.6i	0.0465793	−	0.0806778i
$836$	306293.	+	47262.8i	0.438253	+	0.0676250i
$837$		0			0
$838$	−46957.4	+	612229.i	−0.0668677	+	0.871818i
$839$	21529.2	+	12429.9i	0.0305846	+	0.0176580i	0.515214	−	0.857061i	$-0.327712\pi$
$839$	21529.2	+	12429.9i	0.0305846	+	0.0176580i	−0.484630	+	0.874719i	$0.661046\pi$
$840$		0			0
$841$	−353406.	−	612116.i	−0.499668	−	0.865450i
$842$	459799.	+	959071.i	0.648551	+	1.35278i
$843$		0			0
$844$	156760.	−	195166.i	0.220065	−	0.273980i
$845$		−	35429.8i		−	0.0496199i
$846$		0			0
$847$		−	538205.i		−	0.750207i
$848$	−712451.	−	778697.i	−0.990748	−	1.08287i
$849$		0			0
$850$	−197243.	+	94562.5i	−0.273001	+	0.130882i
$851$	156372.	+	270844.i	0.215923	+	0.373990i
$852$		0			0
$853$	−264635.	−	152787.i	−0.363705	−	0.209985i	0.307000	−	0.951710i	$-0.400675\pi$
$853$	−264635.	−	152787.i	−0.363705	−	0.209985i	−0.670705	+	0.741724i	$0.734008\pi$
$854$	−77648.4	+	1.01238e6i	−0.106467	+	1.38812i
$855$		0			0
$856$	125462.	−	536686.i	0.171224	−	0.732442i
$857$	221670.	−	383944.i	0.301818	−	0.522764i	−0.674730	−	0.738065i	$-0.735740\pi$
$857$	221670.	−	383944.i	0.301818	−	0.522764i	0.976548	+	0.215301i	$0.0690732\pi$
$858$		0			0
$859$	228055.	+	395003.i	0.309067	+	0.535320i	0.978159	−	0.207860i	$-0.0666498\pi$
$859$	228055.	+	395003.i	0.309067	+	0.535320i	−0.669091	+	0.743180i	$0.733317\pi$
$860$	59295.9	−	23032.8i	0.0801729	−	0.0311423i
$861$		0			0
$862$	−422610.	+	617531.i	−0.568755	+	0.831083i
$863$			432830.i			0.581160i	0.956851	+	0.290580i	$0.0938483\pi$
$863$			432830.i			0.581160i	−0.956851	+	0.290580i	$0.906152\pi$
$864$		0			0
$865$	32854.2			0.0439095
$866$	833589.	+	570470.i	1.11152	+	0.760672i
$867$		0			0
$868$	−107413.	−	276526.i	−0.142567	−	0.367026i
$869$	59661.6	−	34445.6i	0.0790052	−	0.0456136i
$870$		0			0
$871$	−1.07933e6	−	623151.i	−1.42272	−	0.821405i
$872$	−1.23138e6	−	287861.i	−1.61941	−	0.378573i
$873$		0			0
$874$	352545.	+	27039.9i	0.461522	+	0.0353983i
$875$	83679.4	−	144937.i	0.109296	−	0.189305i
$876$		0			0
$877$	−439842.	+	253943.i	−0.571870	+	0.330169i	−0.757896	−	0.652376i	$-0.773773\pi$
$877$	−439842.	+	253943.i	−0.571870	+	0.330169i	0.186026	+	0.982545i	$0.440439\pi$
$878$	−276379.	−	576485.i	−0.358522	−	0.747823i
$879$		0			0
$880$	−27468.4	−	30022.6i	−0.0354706	−	0.0387688i
$881$	630033.			0.811730			0.405865	−	0.913933i	$-0.366970\pi$
$881$	630033.			0.811730			0.405865	+	0.913933i	$0.366970\pi$
$882$		0			0
$883$	−111488.			−0.142990			−0.0714950	−	0.997441i	$-0.522777\pi$
$883$	−111488.			−0.142990			−0.0714950	+	0.997441i	$0.522777\pi$
$884$	−223127.	−	179218.i	−0.285527	−	0.229339i
$885$		0			0
$886$	−1.10237e6	+	528498.i	−1.40430	+	0.673249i
$887$	−642963.	+	371215.i	−0.817220	+	0.471822i	−0.849457	−	0.527658i	$-0.823070\pi$
$887$	−642963.	+	371215.i	−0.817220	+	0.471822i	0.0322369	+	0.999480i	$0.489737\pi$
$888$		0			0
$889$	4379.84	−	7586.11i	0.00554185	−	0.00959877i
$890$	−69037.9	−	5295.15i	−0.0871581	−	0.00668495i
$891$		0			0
$892$	126322.	−	818649.i	0.158763	−	1.02889i
$893$	1.11427e6	+	643324.i	1.39729	+	0.806727i
$894$		0			0
$895$	43109.6	−	24889.4i	0.0538181	−	0.0310719i
$896$	−9230.17	+	753711.i	−0.0114972	+	0.938834i
$897$		0			0
$898$	−1.11624e6	−	763905.i	−1.38422	−	0.947298i
$899$	−8736.86			−0.0108103
$900$		0			0
$901$			365754.i			0.450546i
$902$	−396235.	−	271165.i	−0.487012	−	0.333289i
$903$		0			0
$904$	−1.00506e6	+	304251.i	−1.22985	+	0.372302i
$905$	71052.5	+	123067.i	0.0867525	+	0.150260i
$906$		0			0
$907$	−120922.	+	209443.i	−0.146991	+	0.254596i	−0.930114	−	0.367271i	$-0.880292\pi$
$907$	−120922.	+	209443.i	−0.146991	+	0.254596i	0.783123	+	0.621867i	$0.213626\pi$
$908$	892768.	+	137759.i	1.08285	+	0.167090i
$909$		0			0
$910$	108407.	+	8314.74i	0.130911	+	0.0100407i
$911$	−276542.	−	159661.i	−0.333214	−	0.192381i	0.324053	−	0.946039i	$-0.394954\pi$
$911$	−276542.	−	159661.i	−0.333214	−	0.192381i	−0.657267	+	0.753658i	$0.728288\pi$
$912$		0			0
$913$	−68714.8	−	119017.i	−0.0824344	−	0.142781i
$914$	−11838.4	+	5675.58i	−0.0141710	+	0.00679388i
$915$		0			0
$916$	−705177.	−	566407.i	−0.840440	−	0.675053i
$917$		−	491312.i		−	0.584277i
$918$		0			0
$919$		−	1.48790e6i		−	1.76175i	−0.473350	−	0.880875i	$-0.656955\pi$
$919$		−	1.48790e6i		−	1.76175i	0.473350	−	0.880875i	$-0.343045\pi$
$920$	−33865.9	−	31755.4i	−0.0400117	−	0.0375181i
$921$		0			0
$922$	−429439.	−	895745.i	−0.505173	−	1.05371i
$923$	487151.	+	843771.i	0.571821	+	0.990424i
$924$		0			0
$925$	674422.	+	389378.i	0.788222	+	0.455080i
$926$	−197837.	−	15173.9i	−0.230721	−	0.0176961i
$927$		0			0
$928$	20593.1	+	8290.78i	0.0239125	+	0.00962719i
$929$	−588618.	+	1.01952e6i	−0.682028	+	1.18131i	0.292333	+	0.956317i	$0.405569\pi$
$929$	−588618.	+	1.01952e6i	−0.682028	+	1.18131i	−0.974361	+	0.224991i	$0.927765\pi$
$930$		0			0
$931$	50780.5	+	87954.5i	0.0585865	+	0.101475i
$932$	−418986.	−	1.07864e6i	−0.482356	−	1.24178i
$933$		0			0
$934$	−61819.9	−	42306.7i	−0.0708654	−	0.0484970i
$935$			14101.6i			0.0161304i
$936$		0			0
$937$	904036.			1.02969			0.514845	−	0.857283i	$-0.327849\pi$
$937$	904036.			1.02969			0.514845	+	0.857283i	$0.327849\pi$
$938$	642434.	−	938746.i	0.730168	−	1.06695i
$939$		0			0
$940$	−61169.1	−	157474.i	−0.0692271	−	0.178219i
$941$	−569128.	+	328586.i	−0.642733	+	0.371082i	−0.785666	−	0.618650i	$-0.787680\pi$
$941$	−569128.	+	328586.i	−0.642733	+	0.371082i	0.142934	+	0.989732i	$0.454346\pi$
$942$		0			0
$943$	−474393.	−	273891.i	−0.533476	−	0.308003i
$944$	−1.29064e6	−	408023.i	−1.44831	−	0.457868i
$945$		0			0
$946$	−22513.4	+	293528.i	−0.0251570	+	0.327995i
$947$	−100820.	+	174625.i	−0.112420	+	0.194718i	−0.916746	−	0.399471i	$-0.869194\pi$
$947$	−100820.	+	174625.i	−0.112420	+	0.194718i	0.804325	+	0.594189i	$0.202527\pi$
$948$		0			0
$949$	−1.64752e6	+	951194.i	−1.82935	+	1.05618i
$950$	793918.	−	380621.i	0.879688	−	0.421741i
$951$		0			0
$952$	178671.	−	190547.i	0.197143	−	0.210246i
$953$	638389.			0.702910			0.351455	−	0.936205i	$-0.385687\pi$
$953$	638389.			0.702910			0.351455	+	0.936205i	$0.385687\pi$
$954$		0			0
$955$	−107011.			−0.117333
$956$	−1.24533e6	−	1.00027e6i	−1.36260	−	1.09446i
$957$		0			0
$958$	685349.	+	1.42953e6i	0.746759	+	1.55763i
$959$	−213075.	+	123019.i	−0.231684	+	0.133763i
$960$		0			0
$961$	−380552.	+	659136.i	−0.412067	+	0.713721i
$962$	−77919.4	+	1.01591e6i	−0.0841967	+	1.09775i
$963$		0			0
$964$	−414571.	−	63970.8i	−0.446113	−	0.0688379i
$965$	−63737.0	−	36798.6i	−0.0684443	−	0.0395163i
$966$		0			0
$967$	961591.	−	555175.i	1.02834	−	0.593714i	0.111833	−	0.993727i	$-0.464328\pi$
$967$	961591.	−	555175.i	1.02834	−	0.593714i	0.916509	+	0.400013i	$0.130995\pi$
$968$	−716590.	+	216927.i	−0.764751	+	0.231506i
$969$		0			0
$970$	−12299.5	+	17972.4i	−0.0130721	+	0.0191013i
$971$	1.25193e6			1.32783			0.663913	−	0.747810i	$-0.268895\pi$
$971$	1.25193e6			1.32783			0.663913	+	0.747810i	$0.268895\pi$
$972$		0			0
$973$			382787.i			0.404326i
$974$	−542765.	+	793106.i	−0.572129	+	0.836013i
$975$		0			0
$976$	1.37922e6	−	304660.i	1.44788	−	0.319827i
$977$	−33214.5	−	57529.3i	−0.0347968	−	0.0602698i	0.848103	−	0.529832i	$-0.177745\pi$
$977$	−33214.5	−	57529.3i	−0.0347968	−	0.0602698i	−0.882899	+	0.469562i	$0.844412\pi$
$978$		0			0
$979$	160219.	−	277508.i	0.167167	−	0.289541i
$980$	2033.60	−	13179.0i	0.00211745	−	0.0137224i
$981$		0			0
$982$	59980.7	−	782026.i	0.0621997	−	0.810957i
$983$	130314.	+	75236.9i	0.134860	+	0.0778617i	0.565912	−	0.824465i	$-0.308524\pi$
$983$	130314.	+	75236.9i	0.134860	+	0.0778617i	−0.431052	+	0.902327i	$0.641857\pi$
$984$		0			0
$985$	41815.2	+	72426.0i	0.0430984	+	0.0746487i
$986$	−3325.74	−	6936.98i	−0.00342085	−	0.00713538i
$987$		0			0
$988$	898102.	+	721368.i	0.920051	+	0.738997i
$989$			335865.i			0.343378i
$990$		0			0
$991$		−	795870.i		−	0.810391i	−0.914230	−	0.405196i	$-0.867203\pi$
$991$		−	795870.i		−	0.810391i	0.914230	−	0.405196i	$-0.132797\pi$
$992$	−324885.	+	254470.i	−0.330146	+	0.258591i
$993$		0			0
$994$	−801874.	+	384436.i	−0.811584	+	0.389091i
$995$	−93644.4	−	162197.i	−0.0945879	−	0.163831i
$996$		0			0
$997$	674456.	+	389398.i	0.678521	+	0.391745i	0.799298	−	0.600935i	$-0.205205\pi$
$997$	674456.	+	389398.i	0.678521	+	0.391745i	−0.120776	+	0.992680i	$0.538538\pi$
$998$	−80113.1	+	1.04451e6i	−0.0804346	+	1.04870i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.5.p.b.19.35		88
3.2	odd	2		72.5.p.b.43.10	✓	88
4.3	odd	2		864.5.t.b.559.25		88
8.3	odd	2	inner	216.5.p.b.19.6		88
8.5	even	2		864.5.t.b.559.20		88
9.4	even	3	inner	216.5.p.b.91.6		88
9.5	odd	6		72.5.p.b.67.39	yes	88
12.11	even	2		288.5.t.b.79.15		88
24.5	odd	2		288.5.t.b.79.16		88
24.11	even	2		72.5.p.b.43.39	yes	88
36.23	even	6		288.5.t.b.175.16		88
36.31	odd	6		864.5.t.b.847.20		88
72.5	odd	6		288.5.t.b.175.15		88
72.13	even	6		864.5.t.b.847.25		88
72.59	even	6		72.5.p.b.67.10	yes	88
72.67	odd	6	inner	216.5.p.b.91.35		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.p.b.43.10	✓	88	3.2	odd	2
72.5.p.b.43.39	yes	88	24.11	even	2
72.5.p.b.67.10	yes	88	72.59	even	6
72.5.p.b.67.39	yes	88	9.5	odd	6
216.5.p.b.19.6		88	8.3	odd	2	inner
216.5.p.b.19.35		88	1.1	even	1	trivial
216.5.p.b.91.6		88	9.4	even	3	inner
216.5.p.b.91.35		88	72.67	odd	6	inner
288.5.t.b.79.15		88	12.11	even	2
288.5.t.b.79.16		88	24.5	odd	2
288.5.t.b.175.15		88	72.5	odd	6
288.5.t.b.175.16		88	36.23	even	6
864.5.t.b.559.20		88	8.5	even	2
864.5.t.b.559.25		88	4.3	odd	2
864.5.t.b.847.20		88	36.31	odd	6
864.5.t.b.847.25		88	72.13	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.30101 + 2.25906i) q^{2} +(5.79331 + 14.9143i) q^{4} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-14.5686 + 62.3198i) q^{8} +O(q^{10})\)	\(q+(3.30101 + 2.25906i) q^{2} +(5.79331 + 14.9143i) q^{4} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-14.5686 + 62.3198i) q^{8} +(11.6869 + 0.896378i) q^{10} +(-27.1224 + 46.9774i) q^{11} +(-174.611 + 100.811i) q^{13} +(-79.5554 - 165.940i) q^{14} +(-188.875 + 172.807i) q^{16} +88.7146 q^{17} -357.083 q^{19} +(36.5537 + 29.3604i) q^{20} +(-195.656 + 93.8016i) q^{22} +(-214.383 + 123.774i) q^{23} +(-308.207 + 533.830i) q^{25} +(-804.130 - 61.6760i) q^{26} +(112.256 - 727.491i) q^{28} +(-18.7746 - 10.8395i) q^{29} +(349.016 - 201.504i) q^{31} +(-1013.86 + 143.757i) q^{32} +(292.848 + 200.411i) q^{34} -134.813 q^{35} -1263.37i q^{37} +(-1178.73 - 806.671i) q^{38} +(54.3372 + 179.496i) q^{40} +(1106.42 + 1916.37i) q^{41} +(678.384 - 1175.00i) q^{43} +(-857.765 - 132.358i) q^{44} +(-987.293 - 75.7244i) q^{46} +(-3120.48 - 1801.61i) q^{47} +(-142.209 - 246.314i) q^{49} +(-2223.34 + 1065.92i) q^{50} +(-2515.11 - 2020.17i) q^{52} +4122.82i q^{53} +158.955i q^{55} +(2014.00 - 2147.86i) q^{56} +(-37.4881 - 78.1944i) q^{58} +(2643.76 + 4579.12i) q^{59} +(-4778.25 - 2758.72i) q^{61} +(1607.31 + 123.280i) q^{62} +(-3671.51 - 1815.82i) q^{64} +(-295.410 + 511.664i) q^{65} +(3090.68 + 5353.21i) q^{67} +(513.951 + 1323.12i) q^{68} +(-445.019 - 304.551i) q^{70} -4832.30i q^{71} +9435.38 q^{73} +(2854.02 - 4170.38i) q^{74} +(-2068.69 - 5325.66i) q^{76} +(2161.26 - 1247.80i) q^{77} +(-1099.86 - 635.004i) q^{79} +(-226.125 + 715.269i) q^{80} +(-676.901 + 8825.41i) q^{82} +(-1266.75 + 2194.08i) q^{83} +(225.134 - 129.981i) q^{85} +(4893.74 - 2346.16i) q^{86} +(-2532.48 - 2374.66i) q^{88} -5907.27 q^{89} +9275.93 q^{91} +(-3087.99 - 2480.32i) q^{92} +(-6230.78 - 12996.5i) q^{94} +(-906.180 + 523.183i) q^{95} +(-928.999 + 1609.07i) q^{97} +(87.0031 - 1134.34i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 7 q^{2} + 31 q^{4} + 386 q^{8}+O(q^{10}) \) 88 * q - 7 * q^2 + 31 * q^4 + 386 * q^8	\( 88 q - 7 q^{2} + 31 q^{4} + 386 q^{8} - 36 q^{10} - 44 q^{11} + 318 q^{14} + 511 q^{16} + 1156 q^{17} + 860 q^{19} + 1164 q^{20} + 215 q^{22} + 5998 q^{25} + 5232 q^{26} - 516 q^{28} - 5227 q^{32} + 1877 q^{34} + 2508 q^{35} + 4393 q^{38} + 2274 q^{40} - 2348 q^{41} + 3500 q^{43} - 2234 q^{44} + 3576 q^{46} + 16462 q^{49} - 5785 q^{50} - 1440 q^{52} - 1146 q^{56} - 4128 q^{58} + 3508 q^{59} - 2376 q^{62} - 5510 q^{64} + 2502 q^{65} + 5132 q^{67} - 10169 q^{68} + 1134 q^{70} + 19004 q^{73} + 2946 q^{74} - 5875 q^{76} - 8592 q^{80} - 18454 q^{82} - 17090 q^{83} - 18581 q^{86} - 3253 q^{88} + 8272 q^{89} - 9612 q^{91} - 9318 q^{92} - 7590 q^{94} + 9980 q^{97} - 6826 q^{98}+O(q^{100}) \) 88 * q - 7 * q^2 + 31 * q^4 + 386 * q^8 - 36 * q^10 - 44 * q^11 + 318 * q^14 + 511 * q^16 + 1156 * q^17 + 860 * q^19 + 1164 * q^20 + 215 * q^22 + 5998 * q^25 + 5232 * q^26 - 516 * q^28 - 5227 * q^32 + 1877 * q^34 + 2508 * q^35 + 4393 * q^38 + 2274 * q^40 - 2348 * q^41 + 3500 * q^43 - 2234 * q^44 + 3576 * q^46 + 16462 * q^49 - 5785 * q^50 - 1440 * q^52 - 1146 * q^56 - 4128 * q^58 + 3508 * q^59 - 2376 * q^62 - 5510 * q^64 + 2502 * q^65 + 5132 * q^67 - 10169 * q^68 + 1134 * q^70 + 19004 * q^73 + 2946 * q^74 - 5875 * q^76 - 8592 * q^80 - 18454 * q^82 - 17090 * q^83 - 18581 * q^86 - 3253 * q^88 + 8272 * q^89 - 9612 * q^91 - 9318 * q^92 - 7590 * q^94 + 9980 * q^97 - 6826 * q^98

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